Solve 32x^10-97x^5+3=0

$$32 x ^ { 10 } - 97 x ^ { 5 } + 3 = 0$$

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=\sqrt[5]{3}\approx 1.24573094$$

Steps Using the Quadratic Formula

Substitute t for x^{5}.

$$32t^{2}-97t+3=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 32 for a, -97 for b, and 3 for c in the quadratic formula.

$$t=\frac{-\left(-97\right)±\sqrt{\left(-97\right)^{2}-4\times 32\times 3}}{2\times 32}$$

Do the calculations.

$$t=\frac{97±95}{64}$$

Solve the equation t=\frac{97±95}{64} when ± is plus and when ± is minus.

$$t=3 t=\frac{1}{32}$$

Since x=t^{5}, the solutions are obtained by evaluating x=\sqrt[5]{t} for each t.

$$x=\sqrt[5]{3} x=\frac{1}{2}$$